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Seminario di Equazioni Differenziali e Applicazioni: “Convergence rates for monotone numerical schemes for nonlocal Isaacs equations”

Martedì 17 Aprile 2018, ore 12:00 - Aula 2BC30 - Espen Robstad Jakobsen

ARGOMENTI: Seminari

Martedì 17 Aprile 2018 alle ore 12:00 in Aula 2BC30, Espen Robstad Jakobsen (Department of Mathematical Sciences, NTNU, Norway) terrà un seminario dal titolo “Convergence rates for monotone numerical schemes for nonlocal Isaacs equations”.

Abstract
We present new results for monotone numerical schemes for nonlocal Isaacs equations, the dynamic programming equations of stochastic differential games with jump-diffusion state processes. These equations are fully-nonlinear non-convex equations of order less than 2. Here they are also allowed to be degenerate and have non-smooth solutions. The main contribution is a series of new a priori error estimates for a class of monotone numerical methods. These results are (i) the first results for nonlocal Isaacs equations, (ii) the first general results for degenerate non-convex equations of order greater than 1, and (iii) the first results in a viscosity solution setting giving the precise dependence on the fractional order of the equation. We also observe a new phenomena, that the rates differ when the nonlocal diffusion coefficient depend on x and t, only on x, or on neither.
The results are taken from the following paper: [1] I. H. Biswas, I. Chowdhury, and E. R. Jakobsen. On the rate of convergence for monotone numerical schemes for nonlocal Isaacs equations. https://arxiv.org/abs/1709.07743 [arxiv.org] (submitted for publication)

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